Although I generally agree with what you are saying here but in this case I somewhat want to differ about geography and terrain of Bangladesh. Although most of the border of Bangladesh run through plain land but a significant portion also traverse the hilly, jungle areas. Specially in the North East and South Eastern sides. My educated guess is, around 70 percent of our border with India goes over flat land and the rest 30 percent through hilly jungle. Now a significant portion of this flat border also demarcated by international rivers acting as a natural barrier. Moreover, the interior of Bangladesh is criss-crossed by hundreds of rivers and other water bodies posses a significant barrier to invading troops movement. Specially our capital city Dhaka is surrounded by big rivers from all sides. So Bangladesh despite being mostly flat posses significant terrain advantage over invading forces.
In 1971 war, When India fought with Pakistan for liberation of Bangladesh, took 13 days to reach the vicinity of Dhaka despite that fact that Dhaka is barely 100 to 200 km deep from Indian border. Then Indian army enjoyed 10:1 advantage on troops and weapons over Pakistan army deployed in Bangladesh, entire population of Bangladesh welcomed Indian troops, Bengali guerrilla forces fought and provided logistics to Indian army and Indian army engaged in bypassing strategy(avoiding Pakistani defence position to rush into Dhaka). Still it took 13 days! This shows, armored thrust within the interior of Bangladesh is not easy. This is the reason, Bangladesh is often called as the 'defender's paradise'.
This is a double edged sword for India. It is true, Indian landmass surround Bangladesh from 3 sides. But 2 out of this 3 sides covered by Indian land locked north East. An unnatural appendage of Indian mainland precariously connected with mainland India by narrow Siliguri corridor(Chicken neck corridor).
North-east is a part of India which has no sea access and it's 98 percent border is shared with Bangladesh, China and Myanmar and only 2 percent border with Mainland India. India itself has constant headache of defending that part of their country against Chinese military onslaught. Let alone using that part as a launching pad against Bangladesh. A militarily strong Bangladesh will only add headache to Indian defence planners. If somehow, Siliguri corridor can be blocked, then the entire North East will be cut-off from mainland India! India will suffer significant obstacle maintaining normal connectivity between it's mainland theatre and north East theatre of war. So in any hypothetical war with Bangladesh(if Bangladesh can achieve minimum deterrence), Indian forces will be forced to function as a divided front, while Bangladesh, by virtue of being in the middle will operate as a single front with much easier logistics and supply line.
And for the navy part, yes our navy is much weaker than Indian navy. We need some capable submarine fleet to reduce this huge gap and to act as a deterrence. We have no delusion of competing with India in Naval race. We only want enough capability so that India can not attack our coast without heavy losses or block our maritime trade unchallenged. That's it. That's why we need a strong Submarine fleet along with decent number of frigate and corvette.